Fast Solver of Theodorsen equation for conformal mapping


The Transactions of the Korea Information Processing Society (1994 ~ 2000), Vol. 5, No. 2, pp. 372-379, Feb. 1998
10.3745/KIPSTE.1998.5.2.372,   PDF Download:

Abstract

Determinations of conformal mappings from the unit disk onto a Jordan region eventually requires solving the Theodorsen equation which is in general nonlinear with respect to the boundary correspondence function. Among the numerical methods for the Theodorsen equation is the Hubner's method applying the Newton iteraion. His method is well knowen as an efficient one. The reason is that the convergence rate is relatively fast and the memory usage and computation time can ve greatly reduced through the use of FFT(Fast Fourier Transform) However, it has been pointed out that as a result of numercal experiments that the convergence is not so fast for the problems which seem to be highly complicated. In this paper we present a new alternative for fast convergence by applying a low-frequency filter to the Hubner's. As a result, convergence rate is much improved and the filter parameter can be a quantitative measure of the relative difficulty of a given problem.


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Cite this article
[IEEE Style]
S. E. Jee, "Fast Solver of Theodorsen equation for conformal mapping," The Transactions of the Korea Information Processing Society (1994 ~ 2000), vol. 5, no. 2, pp. 372-379, 1998. DOI: 10.3745/KIPSTE.1998.5.2.372.

[ACM Style]
Song En Jee. 1998. Fast Solver of Theodorsen equation for conformal mapping. The Transactions of the Korea Information Processing Society (1994 ~ 2000), 5, 2, (1998), 372-379. DOI: 10.3745/KIPSTE.1998.5.2.372.